Also, let them sue for back wages plus interest and penalties. Those paid below the minimum wage could file with the American Consulate in their home countries with a percentage going to the lawyers who pursue the case to final settlement and the government to defray the costs of illegal immigration.
This would be one way to get some of the lawyers and alien rights advocates on board. A few well-publicized cases would make those businesses who claim they hire illegals because they are such hard workers and not because they can be easily exploited suddenly reconsider their options.